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Partial domain adaptation (PDA), in which we assume the target label space is included in the source label space, is a general version of standard domain adaptation. Since the target label space is unknown, the main challenge of PDA is to reduce the learning impact of irrelevant source samples, named outliers, which do not belong to the target label space. Although existing partial domain adaptation methods effectively down-weigh outliers' importance, they do not consider data structure of each domain and do not directly align the feature distributions of the same class in the source and target domains, which may lead to misalignment of category-level distributions. To overcome these problems, we propose a graph partial domain adaptation (GPDA) network, which exploits Graph Convolutional Networks for jointly considering data structure and the feature distribution of each class. Specifically, we propose a label relational graph to align the distributions of the same category in two domains and introduce moving average centroid separation for learning networks from the label relational graph. We demonstrate that considering data structure and the distribution of each category is effective for PDA and our GPDA network achieves state-of-the-art performance on the Digit and Office-31 datasets.